# Numbering Systems and Codes 230

This class explains how to convert between binary, decimal, octal, and hexadecimal number systems and describes how these systems are used to convey information for PLCs.

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## Class Details

Class Name:
Numbering Systems and Codes 230
Description:
This class explains how to convert between binary, decimal, octal, and hexadecimal number systems and describes how these systems are used to convey information for PLCs.
Version:
1.0
Difficulty:
Intermediate
Number of Lessons:
15
Spanish

## Class Outline

• Objectives
• PLC Numbers
• Numbering Systems
• Decimal System
• Binary System
• Converting Binary to Decimal
• Converting Decimal to Binary
• Binary Arithmetic
• Negative Numbers
• Octal System
• Octal and Binary
• Codes
• BCD System
• Summary

## Objectives

• Describe PLC numbering systems.
• Describe numbering systems.
• Describe the characteristics of the decimal system.
• Describe the characteristics of the binary system.
• Convert binary numbers to decimal numbers.
• Convert decimal numbers to binary numbers.
• Explain how to add binary numbers.
• Describe how negative numbers are represented in binary.
• Convert octal numbers to decimal numbers.
• Convert octal numbers to binary numbers.
• Convert hexadecimal numbers to other number systems.
• Describe the use of number codes in PLCs.
• Describe binary coded decimal.

## Glossary

Vocabulary Term Definition
16-bit Sixteen digits in series.
2s complement The most common method of representing negative binary numbers. If a signed bit contains a "1," all the binary digits are complemented, or reversed, and 1 is added to the number.
8-bit Eight digits in series.
addressing Indicating the location or priority of electrical devices through numerical systems.
alphanumeric Containing letters, numbers, and special symbols found on a PLC input terminal.
ASCII Short for American Standard Code for Information Interchange. ASCII was primarily used to input alphanumeric, punctuation, and control PLC characters, but has been replaced by PC keyboards.
base 10 system The most commonly used number system in everyday life, also known as the decimal system. The base 10 system uses ten digits, 0-9.
base 2 system The most commonly used number system in PLCs and other computer systems, also known as the binary system. The base 2 system has only two digits, 0 and 1.
binary coded decimal A binary number system in which each decimal digit from 0 to 9 is represented by four binary digits (bits). The four positions have a weighted value of 1, 2, 4, and 8, ranging from right to left.
binary system A numbering system that uses two digits, 0 and 1, arranged in a series of columns to represent all numerical quantities. Each column or place value has a weighted value of 1, 2, 4, 8, 16, and so on, ranging from right to left.
bit A single numerical unit in the binary number system. Bit is short for BInary digiT.
byte A series of eight bits.
code Any system that uses digits or symbols to represent information other than simple numerical quantities. Certain code systems are used to allow a PLC to process information more efficiently or with greater accuracy.
complement To reverse binary digits, with all 1s becoming 0s and all 0s becoming 1s. Complementing is a way to represent negative binary numbers.
CPU Central Processing Unit. The CPU is the main device that processes information and carries out instructions in a PLC.
decimal system A numbering system that uses ten digits, from 0 to 9, arranged in a series of columns to represent all numerical quantities. Each column or place value has a weighted value of 1, 10, 100, 1000, and so on, ranging from right to left.
digit Any single character or symbol that is used to represent a numerical quantity.
hexadecimal system A numbering system that uses 16 digits, 0 to 9 and A to F, arranged in a series of columns to represent all numerical quantities. Each column or place value has a weighted value of 1, 16, 256, 4096, and so on, ranging from right to left.
module The physical connection on a PLC where an input or output is plugged in.
multiple Any number that can be evenly divided by a base number, with no remainder.
negative number A number representing a value less than zero. Decimals use a minus sign ( - ) to indicate negative values, but binary numbers must use 2s complement.
nibble Four bits in series, or half an 8-bit byte. A nibble is used to represent decimal numbers in BCD or hexadecimal in binary.
numbering system Any system using a range of digits organized in a series of columns or "places" that represents a specific quantity. The most common numbering systems are decimal, binary, octal, and hexadecimal.
octal system A numbering system that uses eight digits, 0 to 7, arranged in a series of columns to represent all numerical quantities. Each column or place value has a weighted value of 1, 8, 64, 512, and so on, ranging from right to left.
place value The specific column or location of a digit within a numerical system. The place value indicates the specific multiple of the numerical system's base value, or radix.
power A mathematical notation indicating the number of times a quantity is multiplied by itself. Also known as an exponent.
processor The part of the computer that controls the execution of program instructions.
programmable logic controller A processor driven device that uses logic-based software to provide electrical control to machines.
radix The base value indicating the range of digits used to represent numerical quantities in a specific numbering system. The decimal system as a radix of 10 symbols (0 through 9), and the binary system has a radix of 2 (0 and 1).
remainder The quantity left over when one number is divided by another. Remainders are used to maintain whole numbers.
signed bit The most significant bit of a binary number that is used to indicate whether the number is positive or negative. The signed bit must be located one place value beyond the standard set of digits.
significant digit Any digit representing the greater difference between two possible numerical values. In numbering systems, the most significant digit is located farthest to the left.
thumbwheel A rotary device allowing an operator to enter numerical information into a PLC. The operator selects a digit by dialing the thumbwheel.
word A defined and specific number of digits grouped together. For most PLCs, a word consists of 16 digits.